Modeling chemotaxis with nonstandard production/degradation mechanisms from Doebner–Goldin theory: Existence of solitary waves

Abstract

In this paper we investigate various forms of the chemical production–degradation mechanism in a chemotactic system of Keller–Segel type under which the existence of solitary wave solutions is guaranteed. Specifically, the existence of sech-type or compactly supported solitary wave solutions as well as exponential traveling wave profiles for the cell concentration is shown under certain conditions on the physical parameters.